Synopsis and Organizers

Vision is an interdisciplinary field emerged in the early 1980s from psychology, neurosciences, artificial intelligence and applied math. The goal is to study how biological systems, humans and animals, sense and comprehend the environments through their vision; and to build computer systems that can understand objects, scenes and events in images and videos.

From a mathematical perspective, an image has millions of pixels and thus belongs to huge dimensional spaces which are highly heterogeneous and compositional. Natural images contain rich patterns of varying complexities and dimensionalities, from regular man-made structures to stochastic textures in nature. The beauty of these patterns and their underlying mathematical structures have attracted the attentions of mathematicians --- both pure and applied.

The "master" of this workshop, Professor David Mumford, has been studying algebraic geometry as a pure mathematician at Harvard. In 1984, he started his second career in vision, and in 1996 he joined a few applied mathematicians --- Ulf Grenander and Stuart Geman in the pattern theory group at Brown Applied Math Division. His research in vision, together with his students, has generated tremendous impacts to the field.

This workshop will focus on the mathematical aspects of the vision study with the following topics.

• Natural image statistics and regimes of stochastic models;
• Compressive sensing, low-dimensional manifolds and subspace clustering;
• Multi-scale geometric analysis for coding and image processing;
• Theory of 2D and 3D shapes, metrics and diffeomorphism;
• Variational methods and partial differential equations for image analysis;
• Stochastic image grammars and top-down/bottom inference;
• Applications on graphics, visual arts, medical images etc.

The aim of this workshop is to bring together experts in the field to discuss the mathematical issues in vision science and inspire the younger generation to studying these challenging problems.


David MumfordBrown University
Song-Chun ZhuUniversity of California, Los Angeles
David Xianfeng GuState University of New York at Stony Brook
Song-Sun LinNational Chiao Tung University